Adaptive Analog Signal Sampling Through Lagrange Interpolation

Analog signal sampling is one of the most fundamental topics in engineering sciences. The classical Shannon theorem is proposed for the band-limited signals, and so far it has been a cornerstone in signal processing and communication theory. In this work, we present a group of local time domain theorems for sampling differentiable continuous analog signals through Lagrange interpolation, and show how to use them for adaptive control of the sampling rate. Further more, we also discuss the advantages and disadvantages of the proposed time domain adaptive sampling methods. Compared with the Shannon theorem, the proposed methods can guarantee the pointwise reconstruction accuracy with no requirement for the signal bandwidth, and allow efficient adaptive sampling.